cat and mouse

:behavior that is like the way a cat chases a mouse or plays with a mouse before killing it
— used especially to describe a situation in which someone says or does different things to deceive or control other people, to avoid being caught, etc.
— usually used with play

The governor has been playing (a game of) cat and mouse with the media, refusing to say definitely whether he will run for reelection.

The thieves played cat and mouse with the police for several days before they were caught.